Method and apparatus for the estimation of the temperature of a blackbody radiator

ABSTRACT

Remote sensing of the temperature of a greybody or blackbody radiator is effected by passing its radiation ( 24 ) through a modulated infrared filter spectrometer. The infrared filter comprises, in sequence, a band pass filter ( 20 ), a first polariser ( 21 ) which polarises the radiation, an electro-optical element ( 22 ) which splits the polarised radiation into two orthogonally polarised components, and a second polariser ( 23 ). A lens ( 28 ) images the radiation leaving the second polariser onto a detector ( 27 ). The electrical signal from the detector ( 27 ) is input to a numerical analyser. The electro-optical element ( 22 ), typically comprising a birefringent crystal assembly ( 25 ) and a birefringent trim plate ( 26 ), is configured so that the net optical delay of the orthogonally polarised components passed through it is such that the recombined components are at or near a peak or trough in their interferogram. A sinusoidally varying voltage is applied to the electro-optical element to modulate the net delay of the components passed through the electro-optical element. The numerical analyser is programmed to compute the harmonic amplitude ratio (the ratio of signal amplitudes at the fundamental and second harmonic of the frequency of the modulating voltage) of the signal that it receives from the detector ( 27 ). The harmonic amplitude ratio is a function of the temperature of the radiator, which can be estimated by reference to a calibration look-up table.

TECHNICAL FIELD

[0001] This invention concerns the estimation, by remote observation, ofthe temperature of a blackbody or a greybody radiator. Moreparticularly, it involves the estimation of the temperature of aradiator by a relatively low resolution spectral technique, using anovel form of optically filtered and electro-optically modulatedinterferometer. The interferometer or spectrometer (which is one aspectof the present invention), operates in the infrared and/or visibleregion of the electromagnetic spectrum. The method of the inventioninvolves the processing of a selected region of the interferogramproduced by the filter spectrometer.

BACKGROUND TO THE INVENTION

[0002] Non-contact optical thermometry is a rapidly growing field withapplications in remote-sensing of hostile or corrosive environments,medical imaging, environmental studies and industrial processmonitoring. The current best practice in remote temperature sensinginvolves the use of cryogenic infrared radiometers.

[0003] Infrared radiometers are passive sensors operating at wavelengthsnear 10 μm that measure the “brightness temperature” of the infraredradiation emitted by a radiating body in the environment The temperaturesensitivity of an infrared radiometer is determined by its ability toresolve small changes in the radiant emission against background noise.Using sensitive cryogenic quantum well infrared photodetectors (QWIP),temperature sensitivity can be better than 0.02 C.

[0004] If the radiating body is a perfect blackbody (an object with 100%emissivity), the brightness temperature is equal to the physicaltemperature of the radiating body. However, the brightness temperatureis less than the physical temperature for an object with an emissivitybelow 100%. Thus a determination of the physical temperature of aradiating body requires an estimation of the emissivity of the radiator.One consequence of the dependence of the temperature uncertainty onerrors in the estimated emissivity is that a 10% inaccuracy in theestimate of the emissivity can give rise to errors of the order of a fewpercent in the inferred temperature (in degrees Kelvin). In addition,the inferred temperature can be substantially in error if the radiatingsource does not fill the field of view of the measurement system. Thelikelihood of such errors has meant that, in many applications, methodsof temperature measurement which rely on the spectral information arenow preferred over infrared radiometers.

[0005] One spectral technique is two-colour pyrometry. Using thistechnique, the temperature of a radiating body is inferred by measuringthe ratio of the source radiation intensity at two independentwavelengths and applying Planck's radiation law, which states that theblackbody spectral radiance is a universal single parameter distributiongoverned by the temperature T of the radiating source. Planck's law isusually represented by the relationship${H( {v;T} )} = {\frac{2h\quad v^{3}}{c^{2}}\frac{1}{{\exp ( {{hv}/{kT}} )} - 1}}$

[0006] Integrated over wavelength, the total power P radiated by asurface of area A and emissivity ε at temperature T is given by therelationship

P=εAσT⁴

[0007] where σ is the Stefan-Boltzmann constant. In general, theemissivity ε(v,T) is dependent on both wavelength and temperature.

[0008] In two colour pyrometry, the ratio of the power radiated from abody at two selected, narrow wavelength bands is measured. This approachobviates the need for knowledge of the emissivity or its temperaturevariation. However, either (a) the radiating body must be grey (that is,its emissivity is less than 1, and is independent of wavelength), inwhich case ε(v)=ε, or (b) the spectral dependence of ε must be known. Aswell as having a reduced sensitivity to emissivity, ratio pyrometershave the benefit of being insensitive to obscuration of the field ofview due, for example, to dust, smoke, obstruction, or lenscontamination.

[0009] Another technique that relies on being able to treat theradiation source as a greybody, in the sense that the spectral variationof the emissivity is unimportant in the region of interest, isFourier-transform infrared (FTIR) spectroscopy. Fourier transforminfiared spectrometers are usually configured as Michelsoninterferometers in which the translation of one of the mirrors (oftenpiezoelectrically actuated) produces an interference pattern that isregistered by a detector or detector array.

[0010] It was reported, recently, by P. C. Dufour, N. L. Rowell and A.L. Steele, in their paper in Applied Optics, volume 37, 1998, page 5923,that although spectral techniques are not as sensitive to smalltemperature changes as radiometers, FIIR spectrometers are now achievingsub-degree temperature resolution.

[0011] However, current FTIR spectroscopy does have some disadvantages.For example, for optimum performance, FTIR spectrometers must becarefully aligned. They can also be bulky and sensitive to externalnoise, and require a computer for Fourier inversion of the interferogramand display of the spectrum. They are not readily configurable asimaging devices; they have limited field-of-view; and they usuallyrequire optical path length monitoring using a suitable fixed wavelengthsource such as a laser.

[0012] A recently developed spectral instrument is the so-called MOSS(modulated optical solid-state) spectrometer, which monitors the complexcoherence (fringe visibility and phase) of an isolated spectral line atone or more optical delays. This instrument has been used for visiblelight Doppler imaging of high temperature plasmas in the H-1 heliac. TheMOSS spectrometer is described in the specification of Internationalpatent application No. PCT/AU98/00560, which is WIPO Publication No. WO99/04229. It is also featured in the paper by J. Howard, C. Michael, F.Glass and A. Cheetham in Review of Scientific Instruments, volume 72,2001, page 888. More information about the MOSS system, which is usefulin high-resolution studies of spectral lineshape, can be found at theweb address htt://rsphyhsse.anu.edu.au/prl/MOSS.html.

DISCLOSURE OF THE PRESENT INVENTION

[0013] The present invention is a method for measuring the broadbandinfrared blackbody radiation of a body radiating in the infrared and/orvisible region of the electromagnetic spectrum, and an electro-opticalbirefringent plate interferometer for use in such measurement.

[0014]FIG. 1 of the accompanying drawings is a schematic illustration ofa known form of birefringent filter (sometimes called a Lyot filter),with graphical representations of associated features at differentlocations in the optical path through the filter.

[0015] The known filter of FIG. 1 comprises a band pass filter 10, afirst polariser 11, a birefringent plate 12 and a second polariser 13,with the radiation 14A leaving the second polariser being monitored by aphoto-tube (photomultiplier) 19. Assume that the input radiation 14 tothe band pass filter 10 has an amplitude versus wavelength relationship,in the visible and infrared regions of the electromagnetic spectrum, asshown in graphical representation 16 of FIG. 1. The band pass filter 10restricts the radiation incident upon the first polariser 11 to thatwhich lies between the lower and upper wavelengths of the filter 10, asshown in the amplitude versus wavelength graphical representation 17 ofFIG. 1. The first polariser 11 polarises the radiation passing throughit and the birefringent plate 12 splits the polarised light into twocomponents which travel through the birefringent plate at differentvelocities. Thus one of the components of the polarised radiation isdelayed, relative to the other component, within the birefringent plate.

[0016] When the two components leave the birefringent plate, they arecombined by the second polariser 13 to produce a beam 14A of radiationwhich has an amplitude that depends on the net path delay between thecomponents within the birefringent plate 12. Graphical representation 18of FIG. 1 shows how the amplitude of the beam 15 varies with the delaywithin the birefringent plate. The curve depicted in the graphicalrepresentation 18 is known as the interferogram of the filter. The peaksand troughs of the interferogram are known as “fringes”.

[0017] If the birefringent plate is an electro-optical material (thatis, a material which acquires its birefringence by the application of anelectric field; such a phenomenon being known as the Kerr effect, or thePockels effect), the Lyot filter shown in FIG. 1 is known as anelectro-optical filter.

[0018] The present invention, in its apparatus form, is a modified formof the Lyot filter shown in FIG. 1.

[0019] The present invention utilises the fact that, within a narrowfixed wavelength band, the emission intensity is a strong function oftemperature, and the blackbody emission spectrum has a wavelength ofpeak emission λ_(M) (see FIG. 1 of the accompanying drawings), which isuniquely related to the temperature of the blackbody radiator. Thewavelength of peak emission, λ_(M), is given by Wein's displacement law

λ_(M) T=2.898×10⁻³mK.

[0020] Thus, determining λ_(M) or some spectral quantity related to it,allows one to infer the temperature of the source. However, due to theslowly varying nature of the blackbody spectrum with small changes inthe temperature of the radiator, accurate estimation of λ_(M) requiresmeasurements over a significant spectral region.

[0021] The present inventor has recognised that when the temperature ofa radiating blackbody changes, with consequential shifts in λ_(M), theshape of the pass band curve of the graphical representation 17 of FIG.1 changes and, if the filter shown in FIG. 1 is used to observeradiation from the blackbody radiator, the shape of the interferogram ofthe beam 15 (see graphical representation 18) also varies by a smallamount. Furthermore, by the complementarity of time and frequency domainsystems, shifts in λ_(M) should be manifest over a small range ofoptical delay that can be probed with an electro-optical spectrometer.Since the spectral bandwidth required to characterise the blackbodytemperature is wide and the temporal coherence is small, most of thespectral information resides in the interferogram close to zero delay.

[0022] The first spectral moment of the radiation received in a givenspectral pass band (related to λ_(M)) is conveyed by a single measure ofthe interferogram, the interferogram phase. The effective spectral widthof the received radiation is carried by the curvature (fringevisibility) of the interferogram at small delay. Thus changes intemperature of the radiating body result in changes in the phase andfringe visibility of the interferogram.

[0023] Furthermore, measurement of the amplitude and phase of theinterferogram is equivalent to a measurement of the blackbody spectrumin a transmitted pass band. Measurement of the phase is sufficient toinfer the source temperature. Measurement of the amplitude, inconjunction with the Stefan-Boltzmann equation and the temperaturevalue, allows an estimate of the source emissivity to be inferred.

[0024] The present inventor has also appreciated that a modulation ofthe delay in the birefringent plate of the Lyot filter described abovewill generate a modulation in the light intensity sensed by thedetector. Therefore the temporal properties of this modulation of lightintensity can be used to estimate the source temperature, for themeasurement of a single quantity closely related to the phase of theinterferogram near zero delay will provide a direct, robust andunambiguous measure of the source temperature. In particular, it can beshown, by a theoretical analysis (which is provided later in thisspecification), that the ratio of the fundamental (first harmonic) andsecond harmonic amplitudes of the interferogram, near a peak or troughin the interferogram, is related to the phase of the interferogram,which in turn is related to the source temperature through thedimensionless sensitivity factor ρ, which is approximately equal tohv/kT.

[0025] Thus, according to the present invention, a method for theestimation of the temperature of a body emitting radiation in theinfrared and/or visible region of the electromagnetic spectrum comprisesthe steps of

[0026] (a) selecting radiation from said body within a predeterminedwavelength band;

[0027] (b) polarising said selected radiation by passing it through afirst polariser, (c) passing said polarised selected radiation through abirefringent element to split said polarised radiation into first andsecond orthogonally polarised components which travel through saidbirefringent element at differing velocities, so that, on leaving saidelement, there is an optical path length delay of one component relativeto the other component within said birefringent element;

[0028] (d) passing said components through a second polariser to combinesaid components; and

[0029] (e) observing the intensity value at the point in theinterferogram produced by combining said first and second components;

[0030] characterised in that said birefringent element is anelectro-optical birefringent element which is configured so that the netoptical path delay between said first and second components is suchthat, on combination of said components, said intensity value is theintensity value at or near a peak or a trough in said interferogram; andfurther characterised by the additional steps of

[0031] (f) modulating the optical path length delay in saidelectro-optical element, by applying a periodically varied voltage(preferably a sinusoidally varying voltage) to said electro-opticalelement;

[0032] (g) calculating the harmonic amplitude ratio, which is the ratioof the amplitudes of the observed intensity at the fundamental andsecond harmonic of the frequency of the modulating voltage, at theobserved point of the interferogram; and

[0033] (h) determining, from the value of said harmonic amplitude ratio,the temperature of said radiating body by comparing said harmonicamplitude ratio with values of this ratio in a calibration look-uptable.

[0034] Also according to the present invention, there is provided anelectro-optically modulated birefringent filter comprising, in sequence,

[0035] (a) a band pass filter, which permits the passage therethrough ofradiation from a radiating body in a predetermined wavelength band;

[0036] (b) a first polariser;

[0037] (c) an electro-optical element which, when a voltage is appliedto it, splits incident polarised radiation into first and secondorthogonally polarised components which travel through said element atdifferent velocities;

[0038] (d) a second polariser, to combine said components as they exitfrom said electro-optical element; and

[0039] (e) observing means to observe the intensity value at the pointin the interferogram produced by combining said first and secondcomponents;

[0040] characterised in that

[0041] (f) a voltage supply means, adapted to supply a periodicallyvarying voltage, is operatively connected to said electro-opticalelement to produce a modulated the birefringence of said element;

[0042] (g) said electro-optical element is configured so that, in theabsence of an applied modulating voltage, the net optical path lengthdelay between said first and second components is such that, oncombination of said components, said intensity value is the intensityvalue at or near a peak or a trough in said interferogram; and

[0043] (h) said observing means includes means to generate a signalindicative of the observed intensity value, said signal being input toanalysing means which evaluates the harmonic amplitude ratio, which isthe ratio of the amplitudes of the intensity at the fundamental andsecond harmonic of the frequency of the modulating voltage, at theobserved point of the interferogram.

[0044] Preferably, the analysing means is a numerical analyser which isprogrammed to compute the ratio of the peak intensities in the wavepattern of the fringes of said signal output at the fundamental andsecond harmonic frequencies of said modulating voltage, and to comparethis ratio with a calibration look-up table, to determine and displaythe temperature of the radiating body.

[0045] Examples of the electro-optical element that may be used in thepresent invention are:

[0046] (a) a compound electro-optical element consisting of two crosseduniaxial birefringent crystals of nominally equal delay, eachpropagating radiation along the crystal Y-axis, with a bias voltageapplied to produce a predetermined short delay of one of said componentsrelative to the other component;

[0047] (b) a compound electro-optical element consisting of two crosseduniaxial birefringent crystals of nominally equal delay, eachpropagating radiation along the crystal Y-axis, with no bias voltageapplied (and thus with no net birefringence), in series with abirefringent trim plate which produces a predetermined short delay ofone of said components relative to the other component;

[0048] (c) a single electro-optical crystal propagating along theZ-axis, with no bias voltage applied (and thus with no birefringence),in series with a birefringent trim plate to produce a predeterminedshort delay of one of said components relative to the other component;and

[0049] (d) an isotropic electro-optical plate with no bias voltageapplied (and thus with no birefringence), in series with a birefringenttrim plate to produce

[0050] a predetermined short delay of one of said components relative tothe other component.

[0051] Preferably, the frequency of modulation of the optical pathlength is away from the low-frequency “l/f”, or flicker noise associatedwith photoconductors. Modulation of the interferogram signal allows theuse of synchronous detection techniques to improve the signal to noiseratio (SNR), which is inversely proportional to the square root of thedetection bandwidth.

[0052] For a better understanding of the present invention, embodimentsthereof will now be described, by way of example only, with reference tothe accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0053]FIG. 1, as noted earlier in this specification, is a schematicillustration of a known form of birefringent filter (sometimes called aLyot filter), with graphical representations of associated features atdifferent locations in the optical path through the filter.

[0054]FIG. 2 shows the blackbody emission spectra, in the wavelengthband of from 1 to 5 μm, for temperatures spanning 400K to 1000K.

[0055]FIG. 3 depicts interferograms obtained from blackbodies, using theapparatus shown in FIG. 1.

[0056]FIG. 4 is a schematic representation of an electro-optical filterconstructed in accordance with the present invention.

[0057]FIG. 5 shows the variation of the universal blackbody spectrum,and also the variation of the radiometric temperature sensitivity factorρ(x), as a function of the dimensionless parameter x=hv/kT.

[0058]FIG. 6 presents normalised blackbody spectra for temperatures inthe range 600K to 1000K, with a superimposed ideal band pass filter.

[0059]FIG. 7 shows normalised interferograms for the spectra of FIG. 6,for the pass band 3.25 to 3.75 μm.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

[0060] Part of the emission spectra of several blackbody radiators isshown in FIG. 2. If radiation from these radiators is passed through anelectro-optical filter as shown in FIG. 1, with the band pass filter 10being a top hat band pass electro-optical filter, spanning the range offrom 1 to 5 μm, the resultant fringe pattern of the interferogram of theoutput radiation 15 (shown as a plot of intensity of the receivedradiation against the delay introduced by the electro-optical filter) isas shown in FIG. 3. FIG. 3 is, in fact, the Fourier transform of theemission spectra of FIG. 2.

[0061] It is clear from FIG. 1 that, as noted above, it is the shape ofthe interferogram near zero delay that is most closely related to thesource temperature. At the offset delay, or operating point, below thefirst interferogram zero, shown by the region A in the graphicalrepresentation 18 of FIG. 1, the slope of the interferogram increaseswith temperature, while the fringe visibility decreases.

[0062] If the delay in the birefringent element is electro-opticallyscanned about an operating point close to a peak (or trough), thetangent of the appropriately weighted second and first harmonicamplitudes measures the phase in the modulation cycle at which theinterferogram turning point (related to λ_(M)) is encountered. The ratioof the amplitudes of the fundamental frequency and the second harmoniccomponents of the interferogram, generated by modulation of the fringesof the interferogram, is a sensitive measure of the position of theturning point. This ratio of the fimdamental and second harmonicamplitudes of the fringes of the interferogram can be used to estimatetemperature.

[0063] A spectrometer incorporating an electro-optically modulatedbirefringent filter, constructed in accordance with the presentinvention, is illustrated in FIG. 4. It will be apparent that the filtershown in FIG. 4 is a modified form of the electro-optical filter shownin FIG. 1. Since the spectrometer of FIG. 4 is a modulated infraredfilter spectrometer, the present inventor has coined the term “MIRFspectrometer” as a convenient reference term, although it should beapparent to persons of skill in the field of remote sensing that thepresent invention operates outside the infrared portion of theelectromagnetic spectrum.

[0064] The filter of FIG. 4 has an electro-optic element 22 in place ofthe simple birefringent plate of the filter of FIG. 1. Theelectro-optical element 22 is sandwiched between broadband wire grid,plate or dielectric polarisers 21 and 23. The optical delay in thebirefringent crystal is given by τ=LB(λ)/c, where L is the thickness ofthe crystal in the direction of propagation and B(λ)=n_(E)(λ)−n₀(λ) isthe crystal birefringence.

[0065] In the absence of an applied modulating voltage, theelectro-optical element 22 is required to provide only a short delay tothe two polarised radiation components propagating through it. Thus itis preferred that the electro-optical element 22 has one of thefollowing four alternative constructions:

[0066] 1. two crossed uniaxial birefringent crystals, each propagatingradiation along the crystal Y-axis (the so-called Y-cut of the crystals)and having a conventionally applied dc electric field, so that theoptical delays of the crystals almost cancel each other;

[0067] 2. two crossed uniaxial birefringent crystals, each propagatingradiation along the crystal Y-axis, with no applied bias field, but witha separate birefringent plate (called a “trim plate”) in series with thecrossed crystals, to provide a suitable net optical delay offset;

[0068] 3. an electro-optical crystal with radiation propagating alongthe crystal Z-axis) with no bias voltage applied and with a separatebirefringent trim plate in series, to provide a suitable optical delayoffset; and

[0069] 4. an isotropic electro-optical plate, which exhibits nobirefringence in the absence of an applied electric field, with aseparate birefringent “trim plate” in series, to provide a suitableoptical delay offset.

[0070] If the first of these four alternatives is adopted, both lithiumniobate (LiNBO₃) and lithium tantalate (LiTaO₃) are suitable materials,being electro-optic, birefringent and transparent to radiation in therange of visible light to 5 μm. However, because the required netoptical path length delay is small, lithium tantalate, which is weaklybirefringent, is the preferred material. Both of these uniaxial crystalsare naturally birefringent for radiation propagating along the crystalY-axis, and their birefringence can be modified by applying an electricfield in the Z-direction, parallel to the crystal fast axis andtransverse to the direction of propagation. Combining two such crystalswith their fast axes mutually oriented at 90° but with applied electricfields of opposite polarity will subtract their respective delays (togive a small net delay). However, if the applied electric fields ofopposite polarity are modulated, the modulation components will beadded, thereby improving the modulation depth.

[0071] Lithium niobate and lithium tantalate are also the preferredcrystals for the second alternative electro-optic element construction.The “trim plate” is a thin birefringent crystal. Birefringent “trimplates” or “trim pieces” are known components of birefringent systems.The trim plate may be formed integrally with one of the two crossedbirefringent crystals.

[0072] Magnesium fluoride (MgF₂) is another infrared transmissivebirefringent material that is suitable for the construction of a crossedcrystal assembly. Magnesium fluoride is attractive because it has a hightransmissivity at wavelengths of from 100 nm to 8000 nm, a lowrefractive index (1.35), a small, reasonably achromatic birefringenceand a modest temperature coefficient. It should be noted that combiningwaveplates having different material properties allows the constructionof thermally stable compound plates.

[0073] If the fourth alternative arrangement for the electro-opticalelement is adopted, cadmium telluride (CdTe) is a convenient isotropiccrystal to use. If, however, a birefringent crystal oriented forpropagation along the Z-axis is used (the third alternative), lithiumniobate is a suitable crystal material. It has zero naturalbirefringence when propagating radiation along the Z-axis, but theapplication of an electric field along the Y-axis of the Z-cut crystalwill induce a birefringence that can be used to modulate the path lengthdelay in the Z-axis direction. A potential disadvantage of the use of acrystal propagating along the Z-axis is the need to use drive voltages,to produce the required electric field, that can be 30 per cent greaterthan that needed for the crossed Y-cut crystals. Because isotropicand/or Z-cut crystals exhibit no natural birefringence, they are lesssusceptible to thermally induced drifts in the net optical delay. Thisis beneficial for the reliability of the temperature estimate providedby the present invention.

[0074] A voltage supply 29 is connected to the electro-optical element25 to establish the appropriate degree of modulated birefringence whenthe filter of FIG. 4 is in use. Whichever of the alternativearrangements for the electro-optical element is used, the modulation(preferably sinusoidal) of the optical delay in the element 25 iseffected by modulating the amplitude of the voltage applied by thesupply 29 to the birefringent crystal or crystals. If crossedelectro-optical crystals are used, the modulated voltage may be appliedto one of the crystals only. If the modulated voltage is applied to bothof the crystals, a smaller amplitude of the modulation voltage may beapplied to each of the crystals in a manner such that the changes in theoptical delays of the two crystals are cumulative and synchronised.

[0075] A sinusoidal modulation drive voltage can be generated using asimple function generator, a stereo audio amplifier and step-uptransformer. Preferably, the modulation frequency is chosen to match thetime resolution and hardware requirements dictated by the end use of thefilter.

[0076] The input radiation being monitored (beam 24 in FIG. 4) can becoupled directly to the filter or it can be input from an optical fibreand collimating lens combination.

[0077] When the arrangement shown in FIG. 4 is in use, the output beamwill be monitored and processed, in accordance with the method of thepresent invention, to calculate the ratio of the amplitudes of the firstand second harmonics of the modulating voltage frequency, at or near apeak or trough (for example, the region B or C in FIG. 1) of theinterferogram. From the value of this ratio, reference to a calibrationlook-up table will provide an estimate of the temperature of the bodyproducing the input beam of radiation 24.

[0078] The processing of the output beam can be conveniently effected byimaging the output beam onto a detector array, such as a CCD array,which produces an output electrical signal. This electrical signal canbe digitally acquired and submitted to a numerical analyser (a computer)that is programmed to compute the harmonic amplitude ratio. If anabsolute value of the temperature of a radiating body is to bedetermined by a MIRF spectrometer constructed in accordance with thepresent invention, the spectrometer can be calibrated against a knowngreybody to generate a look-up table for the numerical analyser.

[0079] As noted earlier in this specification, a preferred feature ofthe numerical analyser is that it evaluates and displays the amplituderatio or (after calibration of the spectrometer to establish a look-uptable that is stored in the numerical analyser) a temperature value.

[0080] For some applications, it is not essential that the MIRFspectrometer of the present invention is calibrated to give a directreading of the temperature of a radiating body. For example, thespectrometer may be used to monitor a radiating body (perhaps a furnace)that is used in a commercial process which needs to be maintained withina specific temperature range. The analyser can be programmed torecognise when the received signal indicates the harmonic amplituderatio of the radiating body when the process temperature is at itsoptimum value, and to provide an indication (optionally including analarm) when the temperature of the body under observation has changed toa value indicating that the process temperature has departed from itsoptimum value by a predetermined number of degrees. When such adeparture occurs, heat will be supplied to the process (or the processwill be cooled) until the optimum value of the process temperature hasbeen restored.

[0081] As a demonstration of the present invention, a MIRF spectrometerconstructed as shown in FIG. 4 was set up to monitor radiation from afilament light source. The temperature of the filament lamp was a knownfunction of the voltage across the lamp. The electro-optical element wastwo crossed lithium niobate crystals, each having a length of 50 mm anda square aperture of side 25 mm. These crystals were interposed betweentwo broadband red-optimised (620 to 1000 nm) polarizing beamsplittingcubes. In view of the large thicknesses of the lithium niobate crystals,apertures having diameters in the range of from 3 to 5 mm were used tocollimate the beam from the lamp source, to ensure a high instrumentcontrast. A Hamamatsu red-sensitive gallium arsenide photomultipliertube (model R943-02; 200 to 900 nm) was used as detector. A PC-based DAQcard operating under “PC-MOSS” software control was used in conjunctionwith a high voltage amplifier to generate the modulating voltage (at 100Hz) applied to the crystals. The signals were synchronously acquiredusing the same PC-based DAQ system.

[0082] A portion of the interferogram was measured by applying a linearramp of peak amplitude 4000V across the LiNbO₃ crystals. A bias offsetof −2000V was required to compensate for a small mismatch in the crossedcrystal lengths giving rise to incomplete dc cancellation of the opticalpath length. This bias allowed a portion of the interferogram on bothsides of the “white light” position (corresponding to zero net delay) tobe measured. The interferograms were arbitrarily normalized according totheir minimum and maximum peak values.

[0083] The measured interferograms were compared with computedinterferograms for a range of blackbody temperatures. The computation ofinterferograms assumed that only radiation in the band 600 to 900 nmcontributed to the interference signal. There was close similaritybetween the measured and the computed interferograms, includingreasonable agreement about the electro-optic drive voltages required toprobe the interferogram. The minor discrepancies that were observed wereprobably due to the choice of effective optical bandwidth which had beenused for the calculations.

[0084] Using the same experimental arrangement, the sensitivity of theinterferogram to temperature was investigated. A 200 Hz sinusoidalmodulation of amplitude 500V was applied to the dc voltage of 1900Vsupplied to the electro-optic crystals. The temperature of the filamentlamp was varied slowly (that is, in about 10 seconds) by sweeping thefilament voltage. During this sweep of filament voltage, theinterferogram was recorded using the PC-MOSS system, and the ratio offundamental and second harmonic amplitudes was calculated as a functionof filament voltage. The results obtained in this exercise showed thatthe filament voltage could be determined within 0.04V, corresponding toa resolvable temperature change of a few degrees Kelvin. Betterresolution could have been obtained by increasing either the integrationtime (which was 25 milliseconds in these experiments) or the spectralbandwidth.

USES OF THE PRESENT INVENTION

[0085] Because it is a spectrally discriminating device, a MIRFspectrometer incorporating the present invention does not requireabsolute intensity calibration, as is the case for radiometric-basedinstruments such as IR cameras. On the other hand it is much simpler andmore compact than Fourier transform infrared (FTIR) spectrometers, towhich it is related.

[0086] If the instrument is absolutely calibrated, the intensity andphase measurements together can be used to infer the emissivity of theradiating source. Even if not absolutely calibrated, intensity and phasefluctuations taken together can be used to estimate fluctuations insource emissivity. This can have applications in metals manufacturing(for example, in discriminating slag against molten steel).

[0087] When calibrated using a source of known temperature, the presentinvention can be used for remote measurement of the temperature of abody. As an absolute temperature measuring instrument, it is aconvenient and reliable device for calibrating infrared cameras. As aprefilter to a single channel or imaging infrared radiometer, thepresent invention allows the source emissivity to be immediatelydetermined (removal of the MIRF prefilter means that the radiometer maysubsequently be used for sensitive absolute temperature monitoring).When combined with a mid-IR imaging camera and appropriate software, thepresent invention can, in principle, deliver time resolved temperaturecontours of a radiating body.

[0088] If a MIRF spectrometer including the present invention is usedwith an infrared camera and the modulation voltage frequency of thefilter of the spectrometer is an integral sub-harmonic of the frame rateof the IR camera, algebraic manipulation of the images captured insuccessive camera frames enables temperature contours of a body beingimaged to be obtained. If required, the temperature contour informationmay be displayed by the camera.

[0089] A MIRF spectrometer constructed in accordance with the presentinvention, in which the birefringent element is a multicrystal system,with the crystals mounted so that the axis of each crystal is at angleto the crystal axis of the (or each) other crystal in the element, sothat the coherence of the received radiation may be probedsimultaneously at a number of optical delays, may also be usedadvantageously in heat contaminated situations.

[0090] Among the other applications in which the MIRF spectrometer maybe used are:

[0091] 1) industrial process monitoring (including heat treating,forming and extruding, tempering, and the annealing of glass, metals,plastics and rubber, quality control in the food and paper pulpindustries, and curing processes for resins, adhesives and paints;

[0092] 2) non-contact temperature sensors in military, medical,industrial, meteorological, ecological, forestry, agriculture andchemical applications (where regular absolute temperature calibration isessential);

[0093] 3) in an infrared emissivity-based discrimination of missile andaircraft engine spectral signatures;

[0094] 4) in plasma physics, as a monitor of the heat flux to plasmafacing components (first wall and plasma limiting tiles), which aresubjected to loads of up to 5 MW/m in a fusion tokamak; and

[0095] 5) in thermal imaging in medicine (for example in the earlydetection of breast cancer and for locating the cause of circulatorydisorders which lead to local heating and inflammation, which can bedetected with an infrared imager).

[0096] These examples of the use of the present invention are notexhaustive.

BENEFITS OF THE PRESENT INVENTION

[0097] As with other techniques that rely on spectral shape estimationof temperature, a MIRF spectrometer, constructed in accordance with thepresent invention, is not as sensitive to temperature changes as abrightness radiometer. However, particular benefits of the spectrometerof the present invention, compared with other infrared imaging systemsare:

[0098] (a) because it multiplexes spectral information temporally (viathe modulation cycle) rather than onto two separate detector arrays orthrough separate rotating filter elements, the present invention is muchless cumbersome—and less expensive—than dual band (two colour) opticalpyrometers; and

[0099] (b) it is a relatively inexpensive, more compact (and thereforeportable) alternative to mechanically scanned FTIR spectrometers.

THEORETICAL ANALYSIS

[0100] The blackbody spectrum of a radiating source is expressed (seeearlier in this specification) by the relationship${H( {v;T} )} = {\frac{2h\quad v^{3}}{c^{2}}\frac{1}{{\exp ( {{hv}/{kT}} )} - 1}}$

[0101] Using the dimensionless parameter x=hv/kT=hc/λkT, the blackbodyspectrum can be expressed as

H _(υ)(v;T)=αT ³ H(x)   (1)

[0102] Where α is a constant and the universal spectral dependence iscaptured by the function $\begin{matrix}{{H(x)} = \frac{x^{3}}{{\exp \quad x} - 1}} & (2)\end{matrix}$

[0103] This distribution is shown in FIG. 5.

[0104] If the radiator temperature increases incrementally by ΔT, theradiant intensity also increases such that $\begin{matrix}{\frac{\Delta \quad H_{v}}{H_{v}} = {{\rho (x)}\frac{\Delta \quad T}{T}}} & (3) \\{where} & \quad \\{{{\rho (x)} \equiv {\frac{T}{H_{v}}\frac{\partial H_{v}}{\partial T}}} = \frac{x\quad \exp \quad x}{{\exp \quad x} - 1}} & (4)\end{matrix}$

[0105] is the normalised differential radiometric temperaturesensitivity. Note from FIG. 5 that ρ(x)≈x is an excellent approximationover much of the spectrum.

[0106] In the case of a Fourier transform infrared (FTIR) spectrometer,the ideal FTIR signal intensity (interferogram) can be expressed as$\begin{matrix}{{S_{\pm}(\tau)} = {\frac{I_{0}}{2}\lbrack {1 \pm {\lbrack {\gamma (\tau)} \rbrack}} \rbrack}} & (5)\end{matrix}$

[0107] where I₀ is the spectrally integrated emission intensity, τ isthe optical path time delay between interfering wavefronts and γ (τ) isthe optical coherence, related to the light spectral radiance H_(v)(v)through the Weiner-Khinchine theorum $\begin{matrix}{{r(\tau)} = {\frac{1}{I_{0}}{\int_{- \infty}^{\infty}{{H_{v}(v)}{\exp ( {\quad 2\pi \quad v\quad \tau} )}\quad {v}}}}} & (6)\end{matrix}$

[0108] In practice, the maximum fringe visibility (at τ=0) is reduced bythe instrument spectral response to less than unity. This is accountedby multiplying the complex coherence γ by the instrument coherenceγ_(I)=ζ_(I) exp(iφ_(I)) where ζ_(I)<1 is the instrument contrast andφ_(I) the instrument phase. Unless otherwise indicated, it will beassumed that ζ_(I)=1.

[0109] The change in the spectral centre-of-mass with temperature ismanifest as a change in the interferogram carrier frequency. Thevariation gives rise to a temperature-dependent shift in theinterferogram phase which increases with time delay. To estimate thesize of this effect, the optical bandwidth is taken to be sufficientlynarrow to allow a linear approximation to the blackbody spectralradiance at optical frequency v=v₀+δv: $\begin{matrix}{{H_{v}(v)} \approx {H_{0}\lbrack {1 + {{\beta ( x_{0} )}\frac{\delta \quad v}{v_{0}}}} \rbrack}} & (7) \\{where} & \quad \\{{\beta ( x_{0} )} = { {\frac{x_{0}}{H_{0}}\frac{\partial H}{\partial x}} \middle| x_{0}  = {3 - \rho_{0}}}} & (8)\end{matrix}$

[0110] with x₀=hv₀/kT, H₀≡H_(v)(x₀) and ρ₀=ρ(x₀) given by Equation (4)(see also FIG. 5). Substituting Equation (7) into Equation (6) andevaluating the integral gives the interferogram coherence

γ(τ₀ , Δv;T)=ζ_(T)(τ₀ ,Δv)cos [φ₀+φ₉₆(τ₀ ,Δv)]  (9)

[0111] where τ₀=LB(v₀)/c is the interferometer time delay, φ₀=2πv₀τ₀ isthe centre frequency phase delay and the temperature-dependentinterferogram phase shift is given approximately by $\begin{matrix}{{\tan \quad \phi_{T}} = {{( {\rho_{0} - 3} )\frac{\kappa_{0}\phi_{0}}{3}( \frac{\Delta \quad v}{v_{0}} )} \equiv {( {\rho_{0} - 3} )\frac{\hat{\phi}}{3}\frac{\Delta \quad v}{v_{0}}}}} & (10)\end{matrix}$

[0112] where

{circumflex over (φ)}≡κ₀φ₀(Δv/v ₀)=2πτ₀κ₀ Δv   (11)

[0113] is a scaled phase shift coordinate and Δυ is half the opticalbandwidth of the received radiation.

[0114] For a birefringent delay plate of thickness L and birefringenceB(υ), the interferometric time delay at frequency v₀ is given byτ₀=LB(v₀)/c, and the factor $\begin{matrix}{\kappa_{0} =  {1 + {\frac{v_{0}}{B}\frac{\partial B}{\partial v}}} \middle| v_{0} } & (12)\end{matrix}$

[0115] accounts for the wavelength dependence of the birefringence B(υ).

[0116] Expression (10) is valid provided {circumflex over (φ)}²/15<<1.To lowest order, the phase shift is zero when ρ₀=3, corresponding to thepeak of the blackbody curve (ρ_(peak)=2.822).

[0117] While the fringe frequency changes with temperature, the fringecontrast envelope falls quadratically with delay $\begin{matrix}{{\zeta_{T}( {\tau,{\Delta \quad v}} )} = {1 - \frac{{\hat{\phi}}^{2}}{6}}} & (13)\end{matrix}$

[0118] and is insensitive to the temperature to lowest order in Δυ/v₀.As expected, this result shows that the coherence length (the requireddelay for a significant reduction in fringe contrast) is inverselyproportional to the width of the optical pass band. The choice of delayoffset (operating point) φ₀ is a balance between the loss of fringecontrast attending large delay and the temperature-dependent phase shiftφ_(T) which increases with {circumflex over (φ)}.

[0119] The phase modulation, which is applied electro-optically, hasamplitude φ₁ given by $\begin{matrix}{\phi_{1} = {\frac{\pi \quad {ELv}_{0}}{c}\Delta}} & (14)\end{matrix}$

[0120] where E is the electric field strength applied across themodulating element, L is the element length and Δ is a constantcharacterising the strength of the electro-optic effect. When operatingat infrared wavelengths, and for reasonable crystal dimensions andapplied voltages, the phase modulation amplitude φ=φ₁ sin Ωt isgenerally small (≦1). Under these conditions, Equations (9) and (5) canbe combined, and the Bessel expansion used to obtain the amplitude ofthe interferometer signal, S, is given by $\begin{matrix}{S = {\frac{I_{0}}{2}\lbrack {1 + {{J_{0}( \phi_{1} )}\zeta_{c}} - {2{J_{1}( \phi_{1} )}\zeta_{c}\quad \cos \quad 2\Omega \quad t}} \rbrack}} & (15)\end{matrix}$

[0121] where I₀=H_(v)(υ₀)Δυ is the spectrally integrated radiant powerin the measurement pass band and (ζ_(c),ζ_(s))=ζ_(T)[cos(φ_(T)+φ₀),sin(φ_(T)+φ_(T))].

[0122] For modulation about a peak in the interferogram, the modulationsignal predominantly occurs at twice the modulation rate (secondharmonic). When the temperature changes, the peak (or trough) positionalso shifts. The generated signal registers this as a change in theration of fundamental and second harmonic amplitudes. The tangent of theappropriately weighted second and first harmonic amplitudes measures thephase in the modulation cycle at which the interferogram turning point(related to λ_(M)) is encountered. An important advantage of thismeasurement scheme is that the desired information is shifted ontocarriers displaced from dc. As seen in FIG. 3, the position of theinterferogram zero crossing also shifts with temperature. In this case,the information can be extracted from the ratio of the fundamental(modulation amplitude) and dc signal components.

[0123] With the appropriately filtered ideal blackbody spectral radianceH_(v) it is possible to now compute the resulting modulation signaltransform using Equation (6). As an example, the normalised blackbodyspectra for temperatures in the range 600K to 1000K is shown in FIG. 6and their associated interferograms, after filtering by an ideal narrowband pass filter transmitting between 3.25 and 3.75 μm (Δυ/v₀={fraction(1/14)}), are presented in FIG. 7. The interferogram is plotted as afunction of the thickness of a magnesium fluoride waveplate (κ₀=1.267).

[0124] Using Equation (15), the fundamental and second harmonicamplitudes are obtained as

S ₁ =I ₀ζ_(T)(τ₀)J ₁(φ₁)sin φ_(T)   (16)

S ₂ =I ₀ζ_(T)(τ₀)J ₂(φ₁)cos φ_(T)   (17)

[0125] where φ₀≡φ₀ ^((n))2=πv ₀τ_(n), where τ_(n)=n/v₀ corresponds tomodulation about the nth interferogram peak. The weighted ratio of theharmonic amplitudes, Q, is related to the source temperature through itsdependence on the sensitivity factor ρ₀ (see FIG. 5): $\begin{matrix}{Q = {\frac{{J_{2}( \phi_{1} )}S_{1}}{{J_{1}( \phi_{1} )}S_{2}} = {{\tan \quad \phi} = {( {\rho_{0} - 3} )\frac{\hat{\phi}}{3}{( \frac{\Delta \quad v}{v_{0}} ).}}}}} & (18)\end{matrix}$

[0126] It is very significant that in forming the harmonic ratio toobtain φ_(T), any dependence on the emission intensity or the fringecontrast (including instrumental components) has been removed.

ALTERNATIVES AND MODIFICATIONS

[0127] Persons skilled in the field of pyrometry will appreciate thatexamples only of the present invention have been described above, andthat variations to and modifications of the described embodiments may bemade without departing from the present inventive concept.

[0128] One modification of the present invention is to measure aparameter known as the “modulation ratio”, instead of the harmonicamplitude ratio, when observing the recombined components after passagethrough the electro-optical element of the present invention.

[0129] As already noted above, with reference to FIG. 2, if the netdelay of the components within the electro-optical element of thepresent invention is below the first interferogram zero, shown by theregion A in the graphical representation 18 of FIG. 2, the slope of theinterferogram increases with temperature, while the fringe visibilitydecreases. These two effects work in concert so that, at a giventemperature of the radiating body, the variation in the delay lengththat is introduced when the electro-optical crystal of theinterferometer is modulated sinusoidally, produces a variation in theintensity, S, of the detected radiation. The resultant “modulationratio”, ζ, is given by the formula$\zeta = \frac{S_{\max} - S_{\min}}{S_{\max} + S_{\min}}$

[0130] and increases monotonically with temperature. Since the receivedintensity depends on the emissivity and is strongly temperaturedependent, it is necessary to use a normalised measure to indicate theabsolute temperature.

[0131] The modulation ratio ζ is roughly proportional to the amplitudeof the delay modulation while the operating point can also be optimisedfor greater sensitivity to temperature changes within a certaintemperature interval, but with smaller temperature dynamic range.

[0132] Experimental work and theoretical calculations have shown thatthe modulation ratio ζ

[0133] (a) is a function of the temperature of the radiator beingobserved;

[0134] (b) for a given temperature, is dependent on the appliedmodulating voltage (which can be electro-optically tuned within areasonable range by applying an appropriate dc bias voltage); and

[0135] (c) is also dependent on the “operating point” (which is theminimum delay excursion during a modulation cycle).

[0136] Thus, provided the modulating voltage and the operating point areselected to be appropriate values for the temperature of the body beingmonitored, and have fixed values, a measurement of the “modulationratio” provides an indication of the blackbody temperature of the bodybeing monitored.

[0137] The numerical analyser described above can be programmed tocompute the “modulation ratio” with an appropriate algorithm.

[0138] However, the modulation ratio is equivalent to the ratio of theamplitude of the interferogram signal at the voltage modulationfrequency (the fundamental modulation frequency) to the dc amplitude ofthe interferogram signal. This ratio is subject to “flicker noise” or“l/f noise”. Thus this alternative arrangement for monitoring thetemperature of a radiating body is not preferred.

1. A method for the estimation of the temperature of a body emittingradiation in the infrared and/or visible region of the electromagneticspectrum, said method comprising (a) selecting radiation from said bodywithin a predetermined wavelength band; (b) polarising said selectedradiation by passing it through a first polariser; (c) passing saidpolarised selected radiation through a birefringent element to splitsaid polarised radiation into first and second orthogonally polarisedcomponents which travel through said birefringent element at differingvelocities, so that, on leaving said element, there is an optical pathlength delay of one of said polarised components relative to the othercomponent within said birefringent element; (d) passing said componentsthrough a second polariser to combine said components; and (e) observingthe intensity value at the point in the interferogram produced bycombining said first and second components; characterised in that saidbirefringent element is an electro-optical birefringent element which isconfigured so that the net optical path delay between said first andsecond components is such that, on combination of said components, saidintensity value is the intensity value at or near a peak or a trough insaid interferogram; and further characterised by the additional steps of(f) modulating the optical path length delay in said electro-opticalelement, by applying a periodically varied voltage to saidelectro-optical element; (g) calculating the harmonic amplitude ratio,which is the ratio of the amplitudes of the observed intensity at thefundamental and second harmonic of the frequency of the modulatingvoltage, at the observed point of the interferogram; and (h)determining, from the value of said harmonic amplitude ratio, thetemperature of said radiating body by comparing said harmonic amplituderatio with values of this ratio in a calibration look-up table.
 2. Amethod as defined in claim 1, in which said electro-optical element isan electro-optical element selected from the group consisting of: (a)two crossed uniaxial birefringent crystals, each propagating radiationalong the crystal Y-axis, with a bias voltage applied to produce apredetermined short delay of one of said polarised components relativeto the other component; (b) two crossed uniaxial birefringent crystals,each propagating radiation along the crystal Y-axis, with no biasvoltage applied, in series with a birefringent trim plate which producesa predetermined short delay of one of said polarised components relativeto the other component; (c) an electro-optical crystal propagating alongthe Z-axis, with no bias voltage applied, in series with a birefringenttrim plate which produces a predetermined short delay of one of saidpolarised components relative to the other component; and (d) anisotropic electro-optical plate with no bias voltage applied, in serieswith a birefringent trim plate which produces a predetermined shortdelay of one of said polarised components relative to the othercomponent.
 3. A method as defined in claim 1 or claim 2, in which saidperiodically varied voltage is a sinusoidally varied voltage.
 4. Anelectro-optically modulated birefringent filter comprising, in sequence,(a) a band pass filter, which permits the passage therethrough ofradiation from a radiating body in a predetermined wavelength band; (b)a first polariser; (c) an electro-optical element which, when a voltageis applied to it, splits incident polarised radiation into first andsecond orthogonally polarised components which travel through saidelement at different velocities; (d) a second polariser, to combine saidcomponents as they exit from said electro-optical element; and (e)observing means to observe the intensity value at the point in theinterferogram produced by combining said first and second components;characterised in that (f) a voltage supply means, adapted to supply aperiodically varying voltage, is operatively connected to saidelectro-optical element to produce a modulated birefringence of saidelement; (g) said electro-optical element is configured so that, in theabsence of an applied modulating voltage, the net optical path lengthdelay between said first and second components is such that, oncombination of said components, said intensity value is the intensityvalue at or near a peak or a trough in said interferogram; and (h) saidobserving means includes means to generate a signal indicative of theobserved intensity value, said signal being input to analysing meanswhich evaluates the harmonic amplitude ratio, which is the ratio of theamplitudes of the intensity at the fundamental and second harmonic ofthe frequency of the modulating voltage, at the observed point of theinterferogram.
 5. An electro-optically modulated filter as defined inclaim 4, in which said electro-optical element is an electro-opticalelement selected from the group consisting of (a) two crossed uniaxialbirefringent crystals, each propagating radiation along the crystalY-axis, with a bias voltage applied to produce a predetermined shortdelay of one of said polarised components relative to the othercomponent; (b) two crossed uniaxial birefringent crystals, eachpropagating radiation along the crystal Y-axis, with no bias voltageapplied, in series with a birefringent trim plate to produce apredetermined short delay of one of said polarised components relativeto the other component; (d) an electro-optical crystal propagating alongthe Z-axis, with no bias voltage applied, in series with a birefringenttrim plate to produce a predetermined short delay of one of saidpolarised components relative to the other component; and (d) anisotropic electro-optical plate with no bias voltage applied, in serieswith a birefringent trim plate to produce a predetermined short delay ofone of said polarised components relative to the other component.
 6. Anelectro-optically modulated filter as defined in claim 4 or 5, in whichsaid periodically varied voltage is a sinusoidally varied voltage.
 7. Anelectro-optically modulated filter as defined in claim 4 in which saidanalysing means is a numerical analyser which is programmed to computesaid harmonic amplitude ratio.
 8. An electro-optically modulated filteras defined in claim 4 in which said analyzing means is a numericalanalyser which is programmed to compute said harmonic amplitude ratio,compare it with a calibration look-up table stored in said numericalanalyser, and to display the temperature indicated in said look-uptable.
 9. An electro-optically modulated filter as defined in claim 5 inwhich said analysing means is a numerical analyser which is programmedto compute said harmonic amplitude ratio.
 10. An electro-opticallymodulated filter as defined in claim 6 in which said analysing means isa numerical analyser which is programmed to compute said harmonicamplitude ratio.
 11. An electro-optically modulated filter as defined inclaim 5 in which said analyzing means is a numerical analyser which isprogrammed to compute said harmonic amplitude ratio, compare it with acalibration look-up table stored in said numerical analyser, and todisplay the temperature indicated in said look-up table.
 12. Anelectro-optically modulated filter as defined in claim 6 in which saidanalyzing means is a numerical analyser which is programmed to computesaid harmonic amplitude ratio, compare it with a calibration look-uptable stored in said numerical analyser, and to display the temperatureindicated in said look-up table.